short letter vs excuse

short letter and excuse both are nouns.

Word	Noun	Adjective	Verb	Adverb
short letter	Yes	No	No	No
excuse	Yes	No	Yes	No

As nouns, excuse is a hyponym of short letter; that is, excuse is a word with a more specific, narrower meaning than short letter:

short letter (noun)	excuse (noun)
a short personal letter	a poor example
	a defense of some offensive behavior or some failure to keep a promise etc.
	a note explaining an absence

short letter (verb)	excuse (verb)
	accept an excuse for
	defend, explain, clear away, or make excuses for by reasoning
	excuse, overlook, or make allowances for; be lenient with
	serve as a reason or cause or justification of
	grant exemption or release to
	ask for permission to be released from an engagement